This is an announcement for the paper "The embedding of 2-concave Musielak-Orlicz spaces into L_1 via l_2-matrix-averages" by Joscha Prochno.
Abstract: In this note we prove that $\frac{1}{n!} \sum_{\pi} ( \sum_{i=1}^n |x_i a_{i,\pi(i)} |^2)^{\frac{1}{2}}$ is equivalent to a Musielak-Orlicz norm $\norm{x}_{\sum M_i}$. We also obtain the inverse result, i.e., given the Orlicz functions, we provide a formula for the choice of the matrix that generates the corresponding Musielak-Orlicz norm. As a consequence, we obtain the embedding of strictly 2-concave Musielak-Orlicz spaces into L_1.
Archive classification: math.FA
Mathematics Subject Classification: 46B03, 05A20, 46B45
Submitted from: prochno@math.uni-kiel.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.6030
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